Least Squares Matching Pursuit Algorithm Based on Morlet Wavelet

In this paper, we explore the application of the least squares matching pursuit algorithm based on Morlet wavelet. Morlet wavelet is a complex-valued wavelet function and one of the most commonly used wavelets in wavelet analysis. This algorithm aims to achieve signal tracking and localization through wavelet decomposition of signals. During this process, we employ the least squares method for signal fitting and utilize the matching pursuit algorithm to identify signal positions and shapes. The implementation typically involves: 1. Generating Morlet wavelet basis functions with varying scales and translations 2. Applying greedy matching pursuit to select optimal wavelet atoms 3. Using least squares optimization to refine coefficients and minimize residual error 4. Iterating until meeting convergence criteria or reaching maximum iterations This method finds extensive applications in signal processing and image processing fields, including audio signal analysis, image segmentation, and object tracking. By employing the Morlet wavelet-based least squares matching pursuit algorithm, we can achieve more accurate analysis and processing of various types of signals and images. The algorithm's key advantage lies in its ability to provide sparse representations while maintaining high time-frequency resolution through the Morlet wavelet's optimal balance between time and frequency localization.